On a Mixed Finite Element Approximation of the Stokes Problem (I). Convergence of the Approximate Solutions.
O. Pironneau, R. Glowinski (1979)
Numerische Mathematik
Beilin, Sergei A. (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Cavazzoni, Rita (2010)
Boundary Value Problems [electronic only]
Clark, M.R., Lima, O.A. (1997)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Clark, H.R., San Gil Jutuca, L.P., Milla Miranda, M. (1998)
Electronic Journal of Differential Equations (EJDE) [electronic only]
A. Ducrot, V. Volpert (2010)
Mathematical Modelling of Natural Phenomena
In this paper we propose a mathematical model to describe the evolution of leukemia in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous medium. We show the existence of two stationary solutions, one of them corresponds to the normal case and another one to the pathological case. The leukemic state appears as a result of a bifurcation when the normal state loses its stability. The critical conditions of leukemia development are determined by the proliferation...
Sylvia Serfaty (2001)
ESAIM: Control, Optimisation and Calculus of Variations
We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.
Sylvia Serfaty (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We consider an energy-functional describing rotating superfluids at a rotating velocity ω, and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω, and the derivation of a limiting free-boundary problem.
Jean-Claude Saut, Nikolay Tzvetkov (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Jean-Claude Saut, Nikolay Tzvetkov (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We give local and global well-posedness results for a system of two Kadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhu to model the oblique interaction of weakly nonlinear, two dimensional, long internal waves in shallow fluids. We also prove a smoothing effect for the amplitudes of the interacting waves. We use the Fourier transform restriction norms introduced by J. Bourgain and the Strichartz estimates for the linear KP group. Finally we extend the result of [3] for lower...
Takao Sasai (1978)
Journal für die reine und angewandte Mathematik
Hoffmann, Karl-Heinz, Starovoitov, Victor N. (2000)
Documenta Mathematica
Erlangga, Yogi A., Nabben, Reinhard (2008)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Giovanni Prouse (1992)
Banach Center Publications
A Navier-Stokes type equation corresponding to a non-linear relationship between the stress tensor and the velocity deformation tensor is studied and existence and uniqueness theorems for the solution, in the 3-dimensional case, of the Cauchy-Dirichlet problem, for a bounded solution and for an almost periodic solution are given. An inequality which in some sense is the limit of the equation is also considered and existence theorems for the solution of the Cauchy-Dirichlet problems and for a periodic...
Korpusov, M.O., Sveshnikov, A.G. (2005)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Aratyn, Henrik, Gomes, Jose Francisco, Zimerman, Abraham H. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Hideo Kozono, Hermann Sohr (1992)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
V. P. Maslov (1985/1986)
Séminaire Équations aux dérivées partielles (Polytechnique)
A. Bensoussan, L. Boccardo, F. Murat (1988)
Annales de l'I.H.P. Analyse non linéaire
François-Joseph Chatelon, Pierre Orenga (1997)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique